Modulate and Demodulate Function for DSB-TC

Hello,

I am pretty new to matlab and am taking my first communications class where we are discussing AM modulation. I have been trying to simulate a DSB-TC wave in Matlab and for some reason, I get really strange plots. What I am not understanding is the amplitude. Unless I am misunderstanding something. When you demodulate a signal it should always have less amplitude than the original signal. See my plots below. Also I have attached the code. Why is my demodulated signal have a pulse that is so tall at 0?

t=[1:1/100000:10];

m=cos(2*pi*10*t);%exp(-10.*t);%Cont_Cosine(t,1,10);
[f,M]=FourierTransform(t,m);

s_dsbtc=modulate(m,1000, 1000000, 'amdsb-tc',-1);
mhat=demod(s_dsbtc,1000,1000000, 'amdsb-tc',-1);

[f,S_DSBTC]=FourierTransform(t,s_dsbtc);
[f,Mhat]=FourierTransform(t,mhat);

subplot(321);plot(t,m);xlabel('t');ylabel('||m(t)||');title('Message Signal');
subplot(322);plot(f,abs(M));xlabel('f');ylabel('||M(f)||');title('Amplitude Spectrum of Message Signal');

subplot(323);plot(t,s_dsbtc);xlabel('t');ylabel('||S(t)||');title('transmitted signal');
subplot(324);plot(f,abs(S_DSBTC));xlabel('f');ylabel('||S(f)||');title('Amplitude Spectrum transmitted signal');axis([-1000,1000,0,1]);

subplot(325);plot(t,mhat);xlabel('t');ylabel('||mhat(t)||');title('demodulated signal');
subplot(326);plot(f,abs(Mhat));xlabel('f');ylabel('||Mhat(f)||');title('Amplitude Spectrum demodulated signal');